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## Pre-algebra

### Course: Pre-algebra>Unit 8

Lesson 2: Rational number word problems

# Rational number word problem: stock

Use your knowledge of proportions and fractions to determine shareholders profit in this word problem. Created by Sal Khan.

## Video transcript

Shares of stock represent how much of a company a person owns? Puff Incorporated is owned by Peter, Paul, and Mary. Peter owns 4,050 shares, Paul owns 2,510 shares, And Mary owns 42 hundred or 4,200 shares. Suppose the company made a profit this year of \$1,500,000. If each shareholder gets a proportion of the total profit that is equal to the proportion of the share they own, how much money does Mary receive? So first, let's think about what fraction or what percentage or what proportion of the total profit should Mary receive? So Mary owns 4,200 shares. And how many total shares are there in the company? Well, the only owners of this company are Peter, Paul, and Mary. So the total number of shares are the sum of Peter, Paul, and Mary's shares. So we know that Peter owns 4,050 shares. We know that Paul owns 2,510. And of course, we know that Mary owns 4,200. So let's figure it. This is the fraction of the profit that Mary should be getting. So let's figure out this with a calculator. So this is going to be 4,200 divided by 4,050 plus 2,510 plus 4,200. And so Mary should get 0.39 of the profit. Or if we talk about it in terms of percentage, it would be 39% of the profit. So this right over here is 0.390. Actually, let me just leave it like that. So this is approximately equal to 0.39. And so if we want to figure out how much profit she gets, she gets this much times the total profit. So Mary gets 0.39, and this is the exact quantity right over here. 0.39 is the approximation, so approximately 0.39. This little squiggly equal sign is how I say approximately. She's going to get 0.39 times the total profit, which is \$1,500,000. And so let's go back to our calculator. And so we said approximately 0.39. This is the exact value. I can get that exact value again, at least on this calculator, by saying Second Answer. This literally means the previous answer. So this is literally this number right over here-- 0.390334 whatever. So this is the exact quantity times \$1,500,000. One, two, three, there we go. There's \$1,500,000. I've got to make sure I have the right number zeroes there. And that gets us \$585,50- and we need to round to the nearest penny-- and \$0.86. So let me put that someplace where I can see it. So this is going to be equal to \$585,501 and, if we round, \$0.86. So not bad for one year for Mary. She should be able to live quite well just on her dividends from Puff Incorporated.